H

Figure 13. Example of a micromagnetic model with finite element soft-hard grain structure in a two-phase Nd2Fe14B/ Fe3B magnet. Right: Magnetization distribution in a slice plane for zero applied field. The arrows denote the magnetization direction projected on a lice plane. (courtesy of T. Schrefl).

BS nm

Figure 13. Example of a micromagnetic model with finite element soft-hard grain structure in a two-phase Nd2Fe14B/ Fe3B magnet. Right: Magnetization distribution in a slice plane for zero applied field. The arrows denote the magnetization direction projected on a lice plane. (courtesy of T. Schrefl).

characteristic material length parameters: the width of a domain wall, 8W = ^JA/K (where A is the exchange parameter and K is the uniaxial anisotropy strength) and the exchange correlation length Lex = ^JA/M2S, where Ms is the saturation magnetization value. Depending on the value of the anisotropy, these lengths are comparable with or even smaller than the grain sizes of polycrystalline films. If they are smaller, the assumption of a single-domain grain is not always valid. Also and importantly, the thickness of the film could be ignored when the film is thinner that these characteristic lengths. The other problem is that, generally speaking, magnetostatic potential always has a 3D character. The complete 3D calculations are a very time-consuming task and result in a reduced size of a simulated magnetic element. However, in some cases, when the magnetization vector is expected to lay in the plane, the calculations may be restricted to a 2D model [111].

Furthermore, the model could be made much more realistic so as to include explicitly inhomogeneously arranged magnetic moments inside each grain [111, 112], special treatment of boundaries [126], inclusion of magnetically soft phases between hard grains [111, 127], surface roughness [120], etc.

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